/**
 * This program peforms multiplication of two matrices entered by the user.
 * The main method asks for the user to enter two matrices, and then calls
 * multMatrices() to do the multiplication.  The result matrix is then
 * printed.
 */

class Product
{
    public static void main (String[] args)
    { 
       // DECLARE VARIABLES/DATA DICTIONARY

        int[][] a;      // GIVEN:   A matrix of integers
        int[][] b;      // GIVEN:   A matrix of integers
        int aRows;      // GIVEN:   Number of rows in a.
        int aCols;      // GIVEN:   Number of columns in a.
        int bRows;      // GIVEN:   Number of rows in b. 
        int bCols;      // GIVEN:   Number of columns in b.
        int[][] c;      // RESULT:  Product of a and b


        // PRINT OUT IDENTIFICATION INFORMATION
        
        System.out.println();
        System.out.println("ITI 1120 Fall 2006, Lab 10, Example 3");
        System.out.println("Name: Diana Inkpen, Student# 123456");
        System.out.println();


        // READ IN GIVENS

        System.out.println( "Enter the number of rows in matrix A:  " );
        aRows = ITI1120.readInt( );
        System.out.println( "Enter the number of columns in matrix A:  " );
        aCols = ITI1120.readInt( );

        a = MatrixLib.readIntMatrix( aRows, aCols );
        
        System.out.println( "Enter the number of rows in matrix B:  " );
        bRows = ITI1120.readInt( );
        System.out.println( "Enter the number of columns in matrix B:  " );
        bCols = ITI1120.readInt( );

        b = MatrixLib.readIntMatrix( bRows, bCols );

        // BODY OF ALGORITHM
     
        c = multMatrices( a, b );

        // PRINT OUT RESULTS AND MODIFIEDS

        System.out.println( );
        System.out.println( "The product matrix C is: " );
        System.out.println( );
        MatrixLib.printMatrix( c );

    }

    // If the 'main' method calls other algorithms, put the method(s) below.

    /**
     * Performs matrix multiplication on matrices a and b, returning c.
     * 
     * Matrices a and b are assumed to be rectangular, where a is m x n, and
     * b is n x p, for integers m, n, and p.  The resulting matrix c will
     * be m x p.  The dimensions are not passed as parameters; instead,
     * the dimensions are determined from the array lengths.
     * 
     * GIVENS:  a:  an m x n matrix containing integers
     *          b:  an n x p matrix containing integers
     */

    public static int[][] multMatrices( int[][] a, int[][] b )
    {
        // DECLARE VARIABLES / DATA DICTIONARY

        int[][] c;  // RESULT:  the product of matrices a and b
        int aRows;   // INTERMEDIATE:  number of rows in a and c
        int aCols;   // INTERMEDIATE:  number of columns in a, 
        int bRows;   //  INTERMEDIATE: number of rows in b, should be equal to aCols
        int bCols;   // INTERMEDIATE:  number of columns in b and c
        int row;     // INTERMEDIATE:  index for row position in c
        int col;     // INTERMEDIATE:  index for column position in c
        int index;   // INTERMEDIATE:  summation index
        int sum;     // for summing products.
        
        // BODY OF ALGORITHM

        aRows = a.length;       // number of rows in a
        aCols = a[0].length;    // number of cols in a
        bRows = b.length;       // number of rows in b
        bCols = b[0].length;    // number of cols in b
                                // Note: this uses the
                                // assumption that the matrix is a rectangle
                                // so we can can use the length of any row.

        // Create result matrix.  Be careful with dimensions!
        
        c = new int[aRows][bCols];

        // Loop through each matrix position in c:

        for ( row = 0; row < aRows; row = row + 1 )
        {
            for ( col = 0; col < bCols; col = col + 1 )
            {
                // To calculate C[row][col], we need a sum.  Start
                // a running total at 0.
                
                sum = 0;

                // Do the summation
                
                for ( index = 0; index < aCols; index = index + 1 )
                {
                    sum = sum + a[row][index] * b[index][col];
                }
                // At this point, we have the actual c[row][col] value.
                c[row][col] = sum;
                // Go to next position in c.
            }
        }

        // RETURN RESULT

        return c;
    }
                    
}